Problem: The grades on a history midterm at Covington are normally distributed with $\mu = 85$ and $\sigma = 3.0$. Michael earned a n $82$ on the exam. Find the z-score for Michael's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Michael's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{82 - {85}}{{3.0}}} $ ${ z \approx -1.00}$ The z-score is $-1.00$. In other words, Michael's score was $1.00$ standard deviation below the mean.